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Title Algebra Universalis Issue data Basel : Springer Nature Switzerland AG , 2024 ISSN 0002-5240 (print)1420-8911 (online) Form. Descr. časopisy - journals, elektronické časopisy - electronic journals Year, No. Vol. 85 no. 2 (2024) Language English Country Switzerland URL Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 2024: Factor principal congruences and Boolean products in filtral varieties 
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Title Factor principal congruences and Boolean products in filtral varieties Author info Brian A. Davey, Miroslav Haviar Author Davey Brian A. (50%)
Co-authors Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
Source document Algebra Universalis. Vol. 85, no. 19 (2024), pp. 1-23. - Basel : Springer Nature Switzerland AG, 2024 Keywords algebra - algebra Boolean algebra kongruencie Form. Descr. články - journal articles Language English Country Switzerland Annotation Motivated by Haviar and Ploščica's 2021 characterisation of Boolean products of simple De Morgan algebras, we investigate Boolean products of simple algebras in filtral varieties. We provide two main theorems. The first yields Werner's Boolean-product representation of algebras in a discriminator variety as an immediate application. The second, which applies to algebras in which the top congruence is compact, yields a generalisation of the Haviar–Ploščcica result to semisimple varieties of Ockham algebras. The property of having factor principal congruences is fundamental to both theorems. While major parts of our general theorems can be derived from results in the literature, we offer new, self-contained and essentially elementary proofs. URL https://link.springer.com/article/10.1007/s00012-024-00846-8 Public work category ADC No. of Archival Copy 54297 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Algebra Universalis Issue data Basel : Springer Nature Switzerland AG , 2022 ISSN 0002-52401420-8911 Form. Descr. časopisy - journals, elektronické časopisy - electronic journals Year, No. Vol. 83 no. 2 (2022) Language English Country Switzerland URL Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 2022: Canonical extensions of lattices are more than perfect journal
Title Canonical extensions of lattices are more than perfect Author info Andrew P. K. Craig, Maria J. Gouveia, Miroslav Haviar Author Craig Andrew, P. K. (34%)
Co-authors Gouveia Maria Joao (33%)
Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Source document Algebra Universalis. Vol. 83, no. 2 (2022), pp. [1-17]. - Basel : Springer Nature Switzerland AG, 2022 Keywords kanonické rozšírenia matematika - mathematics Form. Descr. články - journal articles Language English Country Switzerland Annotation In a paper published in 2015, we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical exten sions of lattices. Here, we firstly introduce morphisms of TiRS structures and put our correspondence between TiRS graphs and TiRS frames into a full categorical framework. We then answer Problem 2 from our 2015 paper by characterising the perfect lattices that are dual to TiRS frames (and hence TiRS graphs). We introduce a new subclass of perfect lattices called PTi lattices and show that the canonical extensions of lattices are PTi lattices, and so are ‘more’ than just perfect lattices. We illustrate the correspondences between classes of our newly-described PTi lattices and classes of TiRS graphs by examples. We conclude by outlining a direction for future research. URL Link na plný text Public work category ADC No. of Archival Copy 51538 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Algebra Universalis Issue data Basel : Springer Nature Switzerland AG , 2021 ISSN 0002-52401420-8911 Form. Descr. časopisy - journals, elektronické časopisy - electronic journals Year, No. Vol. 82 no. 4 (2021) Language English Country Switzerland URL Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 2021: Perfect extensions of de Morgan algebras journal
Title Perfect extensions of de Morgan algebras Author info Miroslav Haviar, Miroslav Ploščica Author Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
Co-authors Ploščica Miroslav (50%)
Source document Algebra Universalis. Vol. 82, no. 4 (2021), art. no. 58, pp. 1-8. - Basel : Springer Nature Switzerland AG, 2021 Keywords De Morganova algebra - De Morgan algebra MS-algebra rozšírenie - extension Boolean algebra Form. Descr. články - journal articles Language English Country Switzerland Annotation An algebra A is called a perfect extension of its subalgebra B if every congruence of B has a unique extension to A. This terminology was used by Blyth and Varlet [1994]. In the case of lattices, this concept was described by Grätzer and Wehrung [1999] by saying that A is a congruence-preserving extension of B. Not many investigations of this concept have been carried out so far. The present authors in another recent study faced the question of when a de Morgan algebra M is perfect extension of its Boolean subalgebra B(M), the so-called skeleton of M. In this note a full solution to this interesting problem is given. The theory of natural dualities in the sense of Davey and Werner [1983] and Clark and Davey [1998], as well as Boolean product representations, are used as the main tools to obtain the solution. URL Link na plný text Link na zdrojový dokument Public work category ADC No. of Archival Copy 50558 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Algebra universalis Issue data Basel : Springer Nature Switzerland AG , 2020 ISSN 0002-52401420-8911 Form. Descr. časopisy - journals Year, No. Vol. 81 no. 4 (2020) Language English Country Switzerland URL Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 2020: Expanding Belnap: dualities for a new class of default bilattices journal
Title Expanding Belnap: dualities for a new class of default bilattices Author info Andrew P. K. Craig, Brian A. Davey, Miroslav Haviar Author Craig Andrew, P. K. (34%)
Co-authors Davey Brian A. (33%)
Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Source document Algebra universalis. Vol. 81, no. 4 (2020), pp. 1-26. - Basel : Springer Nature Switzerland AG, 2020 Keywords natural duality výsledky - results algebras Form. Descr. články - journal articles Language English Country Switzerland Annotation Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled How a computer should think. Belnap argued that instead of using a logic with two values, for ‘true’ and ‘false’, a computer should use a logic with two further values, for ‘contradiction’ and ‘no information´. The resulting structure is equipped with two lattice orders, a knowledge order and a truth order, and hence is called a bilattice. Prioritised default bilattices include not only values for ‘true’, ‘false’, ‘contradiction’ and ‘no information’, but also indexed families of default values for simultaneous modelling of degrees of knowledge and truth. We focus on a new family of prioritised default bilattices: Jn, for all natural numbers n. The bilattice J0 is precisely Belnap’s seminal example. We obtain a multisorted duality for the variety generated by Jn, and separately a single sorted duality for the quasivariety generated by Jn. The main tool for both dualities is a unified approach that enables us to identify the meet-irreducible elements of the appropriate subuniverse lattices. Our results provide an interesting example where the multi-sorted duality for the variety has a simpler structure than the single-sorted duality for the quasivariety URL Link na zdrojový dokument Public work category ADC No. of Archival Copy 48507 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Algebra Universalis Issue data Cham : Springer Nature Switzerland AG , 2016 ISSN 0002-52401420-8911 Form. Descr. časopisy - journals Year, No. Vol. 76 no. 2 (2016) Language English Country Switzerland URL Link na zdrojový dokument Public work category GII Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References - PERIODIKÁ - Súborný záznam periodika (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika ARTICLES 2016: Piggyback dualities revisited journal
Title Piggyback dualities revisited Author info Davey B. A., Haviar M., Priestley H. A. Author Davey Brian A. (34%)
Co-authors Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Priestley Hilary A. (33%)
Source document Algebra Universalis. Vol. 76, no. 2 (2016), pp. 245-285. - Cham : Springer Nature Switzerland AG, 2016 Keywords duality duality theory Priestley duality Priestleyovská dualita Language English Country Switzerland systematics 51 Public work category ADC No. of Archival Copy 37066 Repercussion category CABRER, Leonardo M. - SPADA, Luca. MV-algebras, infinite dimensional polyhedra, and natural dualities. In Archive for mathematical logic. ISSN 0933-5846, 2017, vol. 56, no. 1-2, pp. 21-42.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article